Following names have to do with either Christmas, December or winter - Carol, Noelle, Noella, Natalie, Natalya, Gloria, Joy, Gioia (italian for Joy), Mary, Maria, Merry, Holly, Angel, Angela, Angelica, Angelika, Gabriella (after the angel Gabriel), Bailey (from the classic holiday movie It's A Wonderful Life), Decima, Bianca, Lucy, Lucia, Persephone, Clementine, Belle, Eve, Eva, Ava, Winter, North, Aspen, Eira(welsh for white as snow), Neve, Neva, Niamh, 

If the baby is born late (which is very likely since those "due dates" by doctors are no more accurate than a fortune tellers and is honestly based on pseudo-science from the 19th century. Also babies can be safely delivered up to 5 weeks "passed their due date") the name January or the spanish Jenara or the italian Gennaio,